Correcting undesired distortions or aberrations and generating desired wavefronts in optical imaging, sensing, signaling and other applications based on bi-valued walsh functions

ABSTRACT

Devices, systems and techniques are provided for adaptive transformation of wavefronts of optical waves or other electromagnetic waves to either correct the undesirable aberration or provide desirable wavefronts or aberrations for various applications, including imaging, sensing, signaling and other applications.

CROSS REFERENCE TO RELATED APPLICATIONS

This patent document is a continuation of U.S. patent application Ser.No. 14/422,163, entitled “CORRECTING UNDESIRED DISTORTIONS ORABERRATIONS AND GENERATING DESIRED WAVEFRONTS IN OPTICAL IMAGING,SENSING, SIGNALING AND OTHER APPLICATIONS BASED ON BI-VALUED WALSHFUNCTIONS” and filed on Feb. 17, 2015, which is a 371 National PhaseApplication of PCT Application No. PCT/US2013/056067, entitled“CORRECTING UNDESIRED DISTORTIONS OR ABERRATIONS AND GENERATING DESIREDWAVEFRONTS IN OPTICAL IMAGING, SENSING, SIGNALING AND OTHER APPLICATIONSBASED ON BI-VALUED WALSH FUNCTIONS” and filed on Aug. 21, 2013, whichclaims the benefit of priority of U.S. Provisional Patent ApplicationNo. 61/691,389, entitled “Transforming and correcting optical wavefrontsfor imaging and other purposes” and filed on Aug. 21, 2012. The entirecontents of the aforementioned patent applications are incorporated byreference as part of the disclosure of this patent document.

TECHNICAL FIELD

This patent document relates to techniques, devices and systems forusing electromagnetic waves including optical waves in imaging, sensingor signaling and other applications.

BACKGROUND

Electromagnetic waves including optical waves can be subject todistortions, aberrations or other perturbations in imaging, sensing orsignaling and other applications. Random and uncontrolled aberrations ofoptical wavefronts are often undesirable as they degrade the performanceof imaging and other optical systems while deliberate and controlledaberrations can be useful in achieving such goals as beam reshaping andcombining.

SUMMARY

Devices, systems and techniques in this patent document are related toadaptive transformation of wavefronts of optical waves or otherelectromagnetic waves to either correct the undesirable aberration orprovide desirable wavefronts or aberrations for various applications,including imaging, sensing, signaling and other applications.

In one implementation, an electromagnetic-field transform system isprovided to employ a wavefront modifier having a plural of controlvariables whose values are optimized from time to time, for achievingand maintaining an intended transform, through adjustments ofWalsh-function amplitudes associated with said values.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an example of an optical system with an adaptive controlbased on bi-valued codes and optical sensing.

FIGS. 2A, 2B and 2C show examples of an optical wavefront modifierhaving actuator elements.

FIGS. 3 and 4 show examples of bi-valued Walsh codes.

FIGS. 5A, 5B and 5C shows three examples for applying Walsh codes tocontrol deformable pixels in an optical wavefront modifier in FIG. 1.

FIG. 6 shows an example of a subroutine for controlling the opticalwavefront modifier in FIG. 1 based on optical sensing and adaptivecontrol based on a performance metric.

FIG. 7 shows an example of a cycling pattern for the modal evaluationand correction routine.

FIG. 8 shows an example of a phase-conjugate correction based on theoptical sensing and adaptive control in FIG. 1. Graphs (a) and (b) arethe phase screen and amplitude screens, respectively; (c) and (d) arePSF in logarithm scale before and after correction, respectively. Theupper right plots show evolutions of Strehl ratio: solid curve is forsevere aberration corrected using the continuous facesheet mirror; thedotted curve is for a weaker aberration corrected using the same mirror;dashed curve is for the same severe aberration corrected using asegmented mirror.

FIG. 9 shows average light intensity of the dark hole as a function ofthe Walsh-mode amplitude. Average light intensity of the dark hole asfunction of the Walsh-mode amplitudes, shown in large scales, (a), andzoom-in, (b). All curves are for the continuous facesheet mirror exceptfor the thin dash line in (a), which is for a segmented mirror.

FIG. 10 shows modal optimization for dark-hole creation. Modaloptimization for dark-hole creation. (a) is the starting PSF under thephase and amplitude aberrations; (b) is after phase-conjugatecorrection; (c) is after dark-hole optimization. The lower left graphshows the diagonal intensity profiles for the three states.

FIG. 11 shows an example implementation of the system in FIG. 1 based ona frequency modulation scheme.

FIG. 12 shows an application of the adaptive control in FIG. 1 in atelescope system.

DETAILED DESCRIPTION

Aberrations of optical wavefronts prevent imaging systems from focusinglight waves into tight spots, resulting in blurry images. Imagingsystems suffer from this effect include microscopes, cameras andtelescopes. In non-imaging optical systems, such as free-space lasercommunication systems, directed energy systems and other beam-formingsystems, random and uncontrolled wavefront aberrations also adverselyaffect the performance of these systems. In other optical systems,aberrations can be deliberately introduced to optical wavefronts forachieving certain objectives such as coherent beam combining and opticaltrapping.

There are existing methods, or prior art, for controlling opticalwavefronts. In an existing technique for correcting aberrated wavefrontsfor imaging, a dedicated wavefront sensing device, or a wavefrontsensor, is employed to characterize the aberration; a wavefrontmodifier, commonly a deformable mirror, is subsequently employed tocorrect the aberration. Drawbacks of this technique include limitedspeeds, poor performance under low-light conditions, limited correctionresolution, inability in providing high-contrast imaging andinapplicability to certain microscopic imaging modalities. There isanother category of existing techniques for correcting aberratedwavefronts that does away with a wavefront sensor by optimizing adeformable mirror under the guidance of a performance metric derivedfrom the system state. These existing techniques typically suffer fromone or more of these drawbacks: slow speeds, stagnation of theoptimization processes, low sensitivity to perturbations of thewavefront modifier and poor wavefront correction resolution. There areexisting techniques for wavefront shaping in non-imaging opticalsystems; these techniques typically involve heavy computation and areslow and suboptimal in the transformations they provide.

Walsh functions can be used for the control of deformable mirror withlight-intensity measurements through single-mode fiber where thewavefront modifiers exert phase adjustments to the optical wavefront inWalsh functions patterns. This requirement can significantly limit theapplicability of the method to deformable mirrors that possess segmentedsurfaces and that provide only piston motions. Also, the number ofcontrolled segments of the deformable mirror is set to be equal to two(2) to the power of an integer and this requirement also restricts theapplicability of the control method.

The disclosed technology in this document can be implemented fortransforming optical wavefronts to serve many imaging or non-imagingpurposes with the characteristics of high speed, high reliability andoptimal transforms.

FIG. 1 shows one example of an optical system having an adaptivecontrol. This system includes an optical wavefront modifier (2)configured to modify at least a spatial phase pattern of an opticalwavefront of an optical input signal (1) to produce a modified opticalsignal (3) having a modified optical wavefront. The optical wavefrontmodifier includes an array of actuator elements at different locationseach operable to modify at least a local phase of the optical wavefrontof the modified optical signal, The actuator elements are coupled toreceive actuator element control signals, respectively, to effectuaterespective local phase values at different locations of the modifiedoptical wavefront. This system includes an optical sensor unit orreceiving optics (4) located in an optical path of the modified opticalsignal from the adaptive optical wavefront modifier and configured toconvert the modified optical signal into an optical sensor signalcontaining information at different locations on the modified opticalwavefront. A control electronic unit (5) is coupled to the opticalsensor unit (4) to receive the optical sensor signal and coupled to theoptical wavefront modifier (2) to generate the actuator element controlsignals based on the optical sensor signal, the control electronic unitconfigured to generate different sets of the actuator element controlsignals based on different sets of bi-valued codes, respectively, togenerate different sets of local phase values at the optical wavefrontmodifier that are adaptive to information in the optical sensor signalreceived at the optical sensor unit over time.

The disclosed wavefront transformation is applicable to a variety ofoptical systems, imaging or non-imaging. In operation of the opticalsystem in FIG. 1, the original wavefront is transformed by the wavefrontmodifier to become the transformed wavefront; the active surface of thewavefront modifier can have a geometrically simple boundary such as asquare or irregular shapes such as the two example patterns in FIG. 1.The surface of the wavefront modifier is composed of segments, each ofwhich can be moved to perturb the optical wavefront. It is should beunderstood that “segments” include areas that can be moved relative totheir surrounding areas in a physically continuous surface.

FIGS. 2A, 2B and 2C show three examples of the wavefront modifier inFIG. 1. FIG. 2A shows a reflective wavefront modifier that includes acontiguous deformable mirror coupled to actuator elements that cause themirror to deform in response to actuator element control signals. FIG.2B shows a reflective wavefront modifier that includes a discretedeformable mirror elements respectively coupled to actuator elementsthat cause the mirror elements to change their positions to effectuate adeformable mirror in response to actuator element control signals. FIG.2C shows a wavefront modifier in FIG. 1 in form of an opticallytransmissive element by using an transmissive spatial phase modulatorthat includes actuator elements that cause different transmissive phaseregions to produce different local phase values in response to actuatorelement control signals.

In a common construction of the wavefront modifier, each of the segmentsis controlled by a discrete control signal. The insert in FIG. 1 showsthe two example patterns for the segments and the associate controlsignals as labeled in numbers. The controlling of the wavefront modifiercalls for movements of the segments in coordinated ways prescribed by agroup of bi-valued functions, namely, the Walsh functions. The Walshfunctions can be considered specific assignation of signs (plus andminus) to arrays of discrete positions. The examples shown in FIG. 3 areWalsh functions for a collection of 32 discrete variables. For a givennumber of independent control valuables, or degrees of freedom, of aphysical system there is always a group of Walsh functions, the totalnumber of which is equal to or greater than the degrees of freedom, thatcompletely describe the state of the system in the sense that anypossible and arbitrary state of the system can be expressed by asuperposition of the Walsh functions. For example, a telescope isequipped with a deformable mirror that is controlled by 225 (in a 15 by15 array) actuators. Any value assignments for the 225 control signalscan be expressed by a superposition of a group of 256 Walsh functions asthey form a mathematically complete and orthogonal basis set for 256numbers, a subset of which (225 numbers) can be associated the realcontrol signals while the remaining numbers are inconsequential.

The use of the Walsh codes for adaptive control of the wavefrontmodifier in FIG. 1 based on optical sensing provides many benefits overother adaptive optical techniques such as wavefront sensing based onpredominantly zonal with the use of Shack-Hartmann sensors which areundesirably insensitive to certain forms of aberration and mirror modes.The bi-valued codes can be used to enable a modal wavefront sensingtechnique as shown in FIG. 1. The basis functions are derived from Walshfunctions. For aberration possessing certain symmetries, such as what isproduced in vision and imaging systems, the polar functions areconvenient to use because they represent some of the commonly existentaberration patterns as defocusing and astigmatism of the first andhigher orders. For adaptive optics systems that are to correctaberration caused by the atmosphere, however, such symmetries do nothelp. In fact, use of the polar functions may be inefficient in themeasurement and correction of the wavefronts in these applications. Theexamples below show the wavefront sensing and correction techniques thatemploy deformable mirrors with pixels arranged in Cartesian arrays,which are found in a large number of adaptive optics systems nowadays.

In one implementation of the adaptive optical system in FIG. 1, thewavefront modifier can be a deformable mirror in a rectangular shapewith N×N pixels. To conveniently generate the orthogonal functions basedon the Walsh series the pixel number should be chosen such that N=2^(η),where η is an integer. This deformable mirror is capable of generatingN×N mutually orthogonal aberration modes in the form of the 2D Walshfunctions, W_(m,n), some of which are shown in FIG. 4. These functionsare binary: they can have only two values, 1 and −1. The indices of thefunctions, m and n, can be arranged in the sequency order, as shown inFIG. 4, so that an ascending index corresponds to an ascending spatialfrequency. The completeness and orthonormality of the Walsh seriesguarantee that any phase function in the rectangular pupil, Φ(x, y), canbe expressed, in the resolution of the given array size, by thefollowing superposition:

${{\Phi ( {x,y} )} = {\sum\limits_{m,n}^{\;}{a_{m,n}W_{m,n}}}},$

The above expansion in the phase space can immediately be converted toan expansion of the electric field in the amplitude space on the samefunctional basis:

${{E( {x,y} )} = {{E_{o}e^{{- j}{\sum\limits_{m,n}^{\;}{a_{m,n}W_{m,n}}}}} = {E_{o}{\sum\limits_{m,n}^{\;}{B_{m,n}W_{m,n}}}}}},$

where each of the coefficients, B_(m,n), is generally dependent on thephase-space coefficients {a_(0,0), a_(0,1), . . . , a_(N,N)}. To correctthe aberration the task is to eliminate all the aberration modes,W_(m,n), from the wavefront.

As shown in FIG. 1, the wavefront modifier can be in differentgeometries and shapes. For a wavefront modifier with M number ofactuator elements, the 2^(n) number of Walsh codes should be greaterthan M number of actuator elements in the wavefront modifier in FIG. 1.FIGS. 5A, 5B and 5C illustrate three examples. In FIG. 5A, a 4-pixeldeformable mirror can be controlled by 4 Walsh codes. In FIGS. 5B and5C, there are some unused Walsh codes.

It many practical cases it is a good approximation to consider that alinear change of a control variable for the wavefront modifier causes alinear change in the optical phase of the corresponding segment. Underthe approximation it can be shown that when the control variables changetheir values in accordance to a Walsh-function pattern the lightintensity of the transformed wavefront at any position varies in asimple sinusoidal fashion. This simple relationship between theperturbation of the control variables and the resultant intensitychanges allows for simple and reliable algorithms that deliver thesystem to an extreme of a performance metric that is derivedarithmetically from light intensities measured from the transformedfield. The sequence of steps shown in FIG. 6 is an exemplary subroutinefor constructing such an algorithm; the boxes in dashed lines indicatesteps that may be omitted. The overall algorithm for achieving aspecific goal usually consists of applying the subroutine to everyWalsh-function patterns. As mentioned previously, the total number ofWalsh-function patterns available for optimization is equal to orgreater than the number of control variables. The use of all theWalsh-function patterns enables the optimal convergence of the wavefrontmodifier; it is, however, unnecessary for all the Walsh-functionpatterns to be controlled in practice because the use of a subgroup ofpredominantly important patterns can sometimes deliver satisfactoryresults.

In the numerical model, the 255 (256 minus the piston mode) modes areupdated following a simple sequence illustrated in FIG. 7. With thesequence, all the modes are given the same frequency of updating andarranged roughly from low spatial frequency to high spatial frequencymodes. These 255 steps form a compensation cycle which can be repeated.The sequence of the first a few low frequency modes is the following:

w_(1,0), w_(0,1), w_(2,0), w_(1,1), w_(0,2) . . . .

At present, adaptive optics (AO) systems rely heavily on computation. Inphase-conjugate AO systems wavefronts are first reconstructed, followedby computing the command signals; in high-contrast imaging electricfields are computed in order for the deformable mirrors to producecountering effects. While these techniques have allowed great advancesthe computations are often major impediments to increasing the speed ofthe systems. AO systems with less or no computation, implementable usinganalog circuits, have been explored since the early days [1]; morerecent effort in this direction has produced remarkable results [2].Questions remain, however, whether analog-control AO can providereliable corrections and whether high-contrast imaging can be realizedwith analog controls at all. In this paper we show that a modaloptimization of deformable mirrors, demonstrated recently, permitsreliable analog control of AO systems for phase-conjugate correctionsand high-contrast imaging.

The proposed computation-free AO is based on a mirror optimizationtechnique using binary modal functions [3,4]. It has been demonstratedin numerical simulation and experiments that, under the guidance offocal-plane metrics, deformable mirrors can be effectively controlledusing binary modes derived from the Walsh functions.

The unique multiplication properties of the Walsh functions provide thefollowing for an optical field in the pupil plane:

$\begin{matrix}{{{U( {x,y} )} = {{U_{o}{\exp ( {{- j}{\sum\limits_{k = 0}^{\infty}{a_{k}W_{k}}}} )}} = {\sum\limits_{k = 0}^{\infty}{b_{k}W_{k}}}}},} & (1)\end{matrix}$

which states that the expansion of the phase function using the Walshfunctions, w_(k), can be converted to a linear superposition of fieldsin modes of the same basis set. This conversion leads to a uniquelysimple relationship between the light intensity in the focal plane andany one modal coefficient:

I=C ₀ +C ₁[sin(a _(k)+φ)]².  (2)

where C₀, C₁ and φ are all independent of a_(k). This equation is validanywhere (on-axis and off-axis) in the focal plane, for any amplitude ofthe modal coefficient, and whether or not there is any amplitudeaberration. For continuous-facesheet mirrors Eq. (2) is a goodapproximation, although it is not strictly obeyed.

Eq. (2) is the mathematical basis for the proposed computation-free AOsystems. For phase-conjugate applications the control electronics shouldbe fashioned to maximize the on-axis light intensity through perturbingthe mirror in all the Walsh-function modes accessible by the mirror. Itcan be shown that the average light intensity in any focal-plane area,such as a dark-hole area, is also governed by Eq. (2). For high-contrastimaging the controller should seek minimization of the intensity in thedark hole. These control goals can be realized with analog circuitryusing the multi-dither principle, in which the mirror is perturbed inthe Walsh-function modes.

Both phase and amplitude aberrations are considered in our simulations.A continuous facesheet mirror with 16×16 actuators is used. The 256actuator heights are adjusted modally using the 256 Walsh-functionmodes. In the simulation, the modes are adjusted individually; asequence of optimizing all the 256 modes constitutes a correction cycle.Shown in FIG. 8 are typical results of maximizing the on-axis intensityfor phase-conjugation. The phase aberration has a RMS value of 0.25λ;the log-amplitude has a mean square deviation of 0.2. It generally takestwo correction cycles for the mirror to converge to a nearly optimalstate; for weak aberrations only one correction cycle is needed.

Substantially more correction cycles are needed for dark holes to beoptimized. This is because the extreme contrasts require extremelyaccurate deformation of the mirror. To create a dark hole in the focalplane the star peak can be first optimized using the phase-conjugateprocedure, followed by the minimization of the average light intensityin the dark hole, or minimization of the inversed contrast.

Phase and amplitude screens similar to the previous example are used insimulating a dark hole creation. A mask of gradual transmission in aSonine function is included as static coronagraph [5]. The generalvalidity of Eq. (2), which encompasses the presence of coronagraphicelements, suggests that the average intensity of a dark-hole varies insinusoidal fashions with changing modal amplitudes. The calculatedresults, shown in FIG. 9, confirm that Eq. (2) is strictly followed fora segmented mirror (the thin dashed curve) and that the relationship isapproximately followed when a continuous-facesheet mirror is used (allother curves).

The results of a simulated dark-hole creation are shown in FIG. 10.Three phase-conjugation cycles boost the contrast from 1.3×10⁻³ to4.0×10⁻⁶. Subsequent 35 cycles of minimizing the light intensity in thedark hole improve the contrast to 2×10⁻⁸. Contrasts on the order of 10⁻⁹to 10⁻¹⁰ have also been obtained using inputs of less severeaberrations.

It is shown that the Walsh-function modes can be used to optimizedeformable mirrors in phase-conjugate and high-contrast imaging. As thecontrol requires neither computation nor knowledge of the coronagraphicoptics it should allow implementations using analog circuitry for highspeeds. The uniquely simple relationship between the cost functions andthe Walsh modal coefficients makes the convergences reliable andvirtually free of local-minimum hazards.

For various applications of wavefront transforms, the performance metriccan be different from one to the other and accordingly the formula fordetermining the appropriate amount of adjustment for the variables, Step6 in the subroutine, can also be different. The following are someexamples:

Phase-Conjugate Correction

In phase-conjugate correction the goal is to best compensate thewavefront aberration. An appropriate performance metric is the lightintensity sensed by one photosensing elements or the average intensitysensed by a group of photosensing pixels. In the presence of a beacon,the pixels upon which the beacon is focused can be used to construct theperformance metric. In the absence of a beacon, the pixels correspondingto a conspicuous spot in the image can be used to construct the beacon.To compensate the aberration in the wavefront, the algorithm should bestructured to maximize the performance metric for each adjustment of thevariables in the Walsh-function patterns.

High-Contrast Imaging

For high-contrast imaging applications, such as the direct observationof faint stellar companions in astronomical imaging, an appropriateperformance metric can be the average light intensity in an observationfield, which is usually adjacent to the focal point of the star, dividedby the intensity of the star. By minimizing this metric the wavefrontmodifier is led to a shape that maximize the dynamic range of imagingfor the chosen observation field.

Fluorescence and Multi-Photon Microscopy

For fluorescence and multi-photon imaging, the performance metric can besimilar to what is employed for phase-conjugate imaging: the lightintensity in pixels that correspond to a conspicuous spot in the imagecan be used as the performance metric. It is the intensity of thefluorescent or the up-converted photons that are measured to form theperformance metric.

Free-Space Laser Communication

The performance metric in this case can simply be the intensity sensedby the photodetector in the receiver.

Optical Trapping and Beam Splitting

To form a plural of movable light spots for optical trapping, theperformance metric can be the summation of the inverses of the lightintensities at the trapping locations. The algorithm should seek theminimization of the metric.

Coherent Beam Combining

To combine a plural of coherent laser beams, the performance metric cansimply be the light energy in the desired direction to which thecombined laser beam propagates.

Due to the algorithmic simplicity, the process of optimizing thewavefront modifier for the above-mentioned applications can beimplemented using analog circuitry or an analog-digital hybrid. Shown inFIG. 11 is an architectural design of the control electronics. Theperformance metric is derived from the receiving optics, typicallyincluding an sensor array or a single photodetector; a functiongenerator is employed to create electric signals, distributed to thecontrol variables in forms of Walsh functions, with combinations of DCand dithering amplitudes. As the optimization of the system isassociated with either the minimization or the maximization of theperformance metric, a circuit can be constructed to seek the DCcomponents that minimize the oscillation of the performance metric atthe fundamental dither frequencies. The use of analog circuits toperform these control tasks can result in fast overall speed of thesystem. These control tasks can also be accomplished with the use ofdigital electronics or a combination of analog and digital electronics.Referring to FIG. 4, more specifically, circuit 5 constructs a signalfrom measured light intensities at one or more locations in thereceiving optics and extract amplitudes of oscillations at a series ofdifferent frequencies; the function generator 7 distributes signals tothe control points of the wavefront modifier in the form ofsuperpositions of a series of Walsh functions, each of which has anindependent amplitude composed of a DC term and a term oscillating atone of the frequencies that is extracted by 5; circuit 6, incommunication with 7, serves to adjust the DC components in theamplitudes of the Walsh functions towards the value that minimizes theamplitudes of the oscillations measured by 5 and corresponds to thedesired outcome.

One of the frontiers of optics today is direct imaging of exoplanets.The extreme contrast in brightness between exoplanets and their parentstars requires precise control of wavefronts from star-planet systems.With the help of adaptive optics (AO) great strides have been madetowards such imaging instruments. Substantial hurdles remain, however,in treating non-ideal pupils, imprecise knowledge of the deformablemirrors and wavefront errors originated from imperfect optics and fromthe atmosphere. The use of sequential deformable mirrors has beenproposed for creating symmetric dark holes, for correcting wavefrontsaberrated in both phase and amplitude, and for use with complex pupilgeometries. Reported methods for controlling sequential deformablemirrors rely on modeling of the optical systems in order to convert theimage-plane measurements to control signals. Reshaping mirror surfacesfor specific purposes can be approached algorithmically throughorthonormal adjustments of the variables in the control space. Thecontrol of two deformable mirrors for high contrast imaging is shown inFIG. 12, which is free of modeling and computation. An additional andstrong motivation of this study is to explore a system analogous to thephase-induced amplitude apodization (PIAA) but without the need forspecialty mirrors.

The imaging system proposed and studied here is schematically shown inFIG. 12. The two deformable mirrors are arranged in a series. Eachdeformable mirror is paired with a conventional (parabolic) mirror whichserves to reduce the strokes of the deformable mirror for broadbandperformance. Both the entrance pupil and the second pupil are assumed tobe hard-edged. The two deformable mirrors are assumed identical,possessing the same influence functions of a continuous face-sheet.There are 1024 actuators for each mirror, arranged in a 32 by 32 squarearray.

In our control algorithm the two deformable mirrors are optimizedtogether based on the feedback from an image-plane metric. For thispurpose a global (engaging all the degrees of freedom of the system) andorthonormal set of 2048 Walsh functions is employed. Superpositions ofthe 2048 functions cover all possible combinations of the 2048 actuatorheights, and therefore, all possible mirror surfaces. The image-planemetric is the integral of light intensity over the hark hole(s) dividedby the on-axis intensity:

${metric} = {\frac{\langle I_{dh}\rangle}{I_{o}}.}$

The control algorithm uses three metric values that are measured undermirror state of the present, the present plus and the present minus aWalsh-function perturbation to the actuator heights, respectively; themetric values then yield an optimizing step for the Walsh-function modewhich involves an adjustment for all the 2048 actuators. Optimizing eachof the 2048 Walsh modes once in a sequence completes an optimizationcycle which is usually repeated.

Our tests indicate that it is feasible to obtain high-contrast PSF usingan optical system with two serially linked deformable mirrors andconventional parabolic mirrors as shown in FIG. 12. The controlalgorithm for the deformable mirrors takes advantage of an orthonormaloptimization scheme in the control space. This system is potentiallyfast, low cost and very flexible as it eliminates two frequent andsignificant burdens: computation and manufacturing of specialty mirrors.In addition, this system is capable of correcting wavefront errors inboth phase and amplitude

While this patent document contains many specifics, these should not beconstrued as limitations on the scope of any invention or of what may beclaimed, but rather as descriptions of features that may be specific toparticular embodiments of particular inventions. Certain features thatare described in this patent document in the context of separateembodiments can also be implemented in combination in a singleembodiment. Conversely, various features that are described in thecontext of a single embodiment can also be implemented in multipleembodiments separately or in any suitable subcombination. Moreover,although features may be described above as acting in certaincombinations and even initially claimed as such, one or more featuresfrom a claimed combination can in some cases be excised from thecombination, and the claimed combination may be directed to asubcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. Moreover, the separation of various system components in theembodiments described in this patent document should not be understoodas requiring such separation in all embodiments.

Only a few implementations and examples are described and otherimplementations, enhancements and variations can be made based on whatis described and illustrated in this patent document.

What is claimed is:
 1. An optical system having an adaptive control,comprising: an optical wavefront modifier configured to modify at leasta spatial phase pattern of an optical wavefront of an optical inputsignal to produce a modified optical signal having a modified opticalwavefront, the optical wavefront modifier including an array of actuatorelements at different locations each operable to modify at least a localphase of the optical wavefront of the modified optical signal, theactuator elements coupled tor receive actuator element control signals,respectively, to effectuate respective local phase values at differentlocations of the modified optical wavefront; an optical sensor unitlocated in an optical path of the modified optical signal from theadaptive optical wavefront modifier and configured to convert themodified optical signal into an optical sensor signal containinginformation at different locations on the modified optical wavefront;and a control electronic unit coupled to the optical sensor unit toreceive the optical sensor signal and coupled to the optical wavefrontmodifier to generate the actuator element control signals based on theoptical sensor signal, the control electronic unit configured togenerate different sets of the actuator element control signals based ondifferent sets of bi-valued codes, respectively, to generate differentsets of local phase values at the optical wavefront modifier that areadaptive to information in the optical sensor signal received at theoptical sensor unit over time.
 2. The system as in claim 1, wherein: thecontrol electronic unit is configured to use first obtained informationin the optical sensor signal received at the optical sensor unit toapply first bi-valued codes to produce first actuator element controlsignals which produce a first modified optical wavefront via the opticalwavefront modifier, and, to subsequently use second obtained informationin the optical sensor signal subsequently received at the optical sensorunit to apply second bi-valued codes different from the first bi-valuedcodes to produce second actuator element control signals which produce asecond modified optical wavefront via the optical wavefront modifierthat is a superposition of the first modified optical wavefront andadditional optical wavefront modification produced by the opticalwavefront modifier associated with the second bi-valued codes.
 3. Thesystem as in claim 2, wherein: in generating respective actuator elementcontrol signals for the first or second bi-valued codes, the controlelectronic unit is configured to process the received optical sensorsignal to generate a signal performance metric for the received opticalsensor signal and uses the signal performance metric and the respectivebi-valued codes to determine intermediate actuator element controlsignals by perturbing the actuator element control signals and measuringthe signal performance metric from the received optical sensor signalcaused by the perturbing of the intermediate actuator element controlsignals.
 4. The system as in claim 3, wherein: the signal performancemetric includes a light intensity at a selected location of the opticalsensor unit.
 5. The system as in claim 3, wherein: the signalperformance metric includes an averaged light intensity at severalselected locations of the optical sensor unit.
 6. The system as in claim3, wherein: the signal performance metric includes an image contrastmeasured at the optical sensor unit.
 7. The system as in claim 2,wherein: the bi-valued codes are bi-valued Walsh codes.
 8. The system asin claim 7, wherein: the control electronic unit is configured to use aportion of selected sets of bi-valued Walsh codes from available sets ofbi-valued Walsh codes.
 9. The system as in claim 8, wherein: the portionof selected sets of bi-valued Walsh codes correspond to low frequencymodes for the modified optical signal.
 10. The system as in claim 8,wherein: the first bi-valued codes are Walsh codes corresponding tolower frequency modes than frequency modes of Walsh modes for the secondbi-valued codes.
 11. The system as in claim 1, wherein: the opticalwavefront modifier includes a deformable mirror which operates toproduce local phase values at different locations by controlling theactuator elements to produce reflected light as the modified opticalsignal.
 12. The system as in claim 1, wherein: the optical wavefrontmodifier includes a spatial light modulator that produces the modifiedoptical signal.
 13. The system as in claim 1, wherein: the opticalwavefront modifier produces the modified optical signal by opticaltransmission.
 14. The system as in claim 1, wherein: the opticalwavefront modifier includes different segments coupled to the actuatorelements, respectively, where the different segments interact differentspatial portions of the optical wavefront to effectuate the respectivelocal phase values at different locations of the modified opticalwavefront.
 15. The system as in claim 1, wherein: the optical wavefrontmodifier includes a continuous surface that is coupled to the actuatorelements, respectively, to effectuate respective local phase values atdifferent locations of the modified optical wavefront.
 16. The system asin claim 1, wherein: the optical sensor unit includes an array ofoptical sensors for sensing the light directed from the opticalwavefront modifier.
 17. A method for operating an optical system havingan adaptive control, comprising: applying actuator element controlsignals to actuator elements at different locations of an opticalwavefront modifier to modify at least a spatial phase pattern of anoptical wavefront of an optical input signal to produce a modifiedoptical signal having a modified optical wavefront, wherein, theactuator elements are operated to effectuate respective local phasevalues at different locations of the modified optical wavefront;measuring the modified optical signal to obtain an optical sensor signalcontaining information at different locations on the modified opticalwavefront; and providing an adaptive control over the optical wavefrontmodifier based on the information at different locations on the modifiedoptical wavefront in the optical sensor signal over time to generatedifferent sets of the actuator element control signals based ondifferent sets of bi-valued codes, respectively, to generate differentsets of local phase values at the optical wavefront modifier over timeto correct undesired distortions in the optical input signal or togenerate desired wavefront modification to the in the optical inputsignal.
 18. The method as in claim 17, comprising: at a first time,using first obtained information in the optical sensor signal to applyfirst bi-valued codes to produce first actuator element control signalswhich produce a first modified optical wavefront via the opticalwavefront modifier, and, at a second time subsequent to the first time,using second obtained information in the optical sensor signal to applysecond bi-valued codes different from the first bi-valued codes toproduce second actuator element control signals which produce a secondmodified optical wavefront via the optical wavefront modifier that is asuperposition of the first modified optical wavefront and additionaloptical wavefront modification produced by the optical wavefrontmodifier associated with the second bi-valued codes.
 19. The method asin claim 17, wherein: in generating respective actuator element controlsignals for the first or second bi-valued codes, the method furthercomprises: processing the optical sensor signal to generate a signalperformance metric; using the signal performance metric and therespective bi-valued codes to determine intermediate actuator elementcontrol signals by perturbing the actuator element control signals andmeasuring the signal performance metric from the received optical sensorsignal caused by the perturbing of the intermediate actuator elementcontrol signals; and based on an impact to the signal performance metriccaused by the perturbing of the intermediate actuator element controlsignals, generating the respective actuator element control signals forthe first or second bi-valued codes.
 20. The method as in claim 17, 18or 19, wherein: the bi-valued codes are bi-valued Walsh codes.
 21. Themethod as in claim 20, further comprising: using only a portion ofselected sets of bi-valued Walsh codes from available sets of bi-valuedWalsh codes in the adaptive control.
 22. The method as in claim 21,comprising: first using bi-valued Walsh codes corresponding to lowfrequency modes for the modified optical signal and then using bi-valuedWalsh codes corresponding to higher frequency modes for the modifiedoptical signal.
 23. The method as in claim 17, comprising: modulatingthe actuator element control signals at different modulation frequenciesthat correspond to different bi-valued codes, respectively; andsimultaneously optimizing the actuator element control signals thatcorrespond to different bi-valued codes, respectively, by measuringsignal components in the optical sensor signal that correspond to thedifferent modulation frequencies.
 24. An electromagnetic-field transformsystem employing a wavefront modifier having a plural of controlvariables whose values are optimized from time to time, for achievingand maintaining an intended transform, through adjustments ofWalsh-function amplitudes associated with said values.
 25. The system asin claim 24, wherein said wavefront modifier is a deformable mirror or aspatial light modulator having a plural of control variables thatdetermine the spatially varied phase modification experienced by theelectromagnetic fields.
 26. An electromagnetic-field transform systememploying a wavefront modifiers having a plural of control variableswhose values are optimized from time to time, under the guidance of aperformance metric whose minimization or maximization corresponds to thefulfillment of the intended transform, through adjustments ofWalsh-function amplitudes associated with said values.
 27. The system asin claim 26, wherein said wavefront modifier is a deformable mirror or aspatial light modulator having a plural of control variables thatdetermine the spatially varied phase modification experienced by theelectromagnetic fields.
 28. An imaging system employing a deformablemirror having a plural of control variables whose values are optimizedfrom time to time through adjustments of Walsh-function amplitudesassociated with said values to maximize or minimize a metric derivedfrom the light intensities measured from the image-forming plane.
 29. Amicroscope system employing a deformable mirror having a plural ofcontrol variables whose values are optimized from time to time throughadjustments of Walsh-function amplitudes associated with said values tomaximize the light emitted by a specimen, under the excitation of anexcitation light, and received by one or a plural of light sensingelements.
 30. A free-space laser communication system employing adeformable mirror having a plural of control variables whose values areoptimized from time to time through adjustments of Walsh-functionamplitudes associated with said values to maximized the light receivedby the photodetector in the receiver.
 31. An optical trapping deviceemploying a deformable mirror or a spatial light modulator having aplural of control variables whose values are optimized from time to timethrough adjustments of Walsh-function amplitudes associated with saidvalues to maximize light intensities at desired locations for trappingobjects.
 32. A laser beam combing system employing a deformable mirrorhave a plural of control variables whose values are optimized from timeto time through adjustments of Walsh-function amplitudes associated withsaid values to maximized the optical energy propagating in a singledirection.
 33. An imaging system employing a deformable mirror having aplural of control variables whose values are optimized from time totime, under the operation of an analog circuit or an analog-digitalhybrid circuit, through adjustments of Walsh-function amplitudesassociated with said values to minimize the oscillations at a plural offrequencies of a metric derived from the light intensities in theimage-forming plane while dithering said control variables in accordanceto said Walsh functions at said frequencies.
 34. A microscope systememploying a deformable mirror having a plural of control variables whosevalues are optimized from time to time, under the operation of an analogcircuit or an analog-digital hybrid circuit, through adjustments ofWalsh-function amplitudes associated with said values to minimize theoscillation at a plural of frequencies of the light emitted, under theexcitation of an excitation light, by a specimen and received by one ora plural of light sensing elements while dithering said controlvariables in accordance to said Walsh functions at said frequencies. 35.A free-space laser communication system employing a deformable mirrorhaving a plural of control variables whose values are optimized fromtime to time, under the operation of an analog circuit or ananalog-digital hybrid circuit, through adjustments of Walsh-functionamplitudes associated with said values to minimize the oscillations at aplural of frequencies of the light received by the photodetector in thereceiver while dithering said control variables in accordance to saidWalsh functions at said frequencies.
 36. An optical trapping deviceemploying a deformable mirror or a spatial light modulator having aplural of control variables whose values are optimized from time totime, under the operation of an analog circuit or an analog-digitalhybrid circuit, through adjustments of Walsh-functions amplitudesassociated with said values to minimize the oscillations at a plural offrequencies of light intensities at desired locations while ditheringsaid control variables in accordance to said Walsh functions at saidfrequencies.
 37. A dynamic diffractive optical device, comprising: avariable wavefront modifier possessing a plural of control points forexerting spatially varied optical path lengths across a beam of light,and a control unit that executes functions including acquiringinformation about the light after encountering said variable wavefrontmodifier and distributing two-valued control signals to said controlpoints in patterns of Walsh functions with amplitudes based on saidinformation.
 38. The device as in claim 37 wherein said variablewavefront modifier is a deformable mirror.
 39. The device as claim 37,wherein said variable wavefront modifier is a spatial light modulator.40. An imaging system, comprising: a lens assembly, a deformable mirrorproviding wavefront modification that is determined by the values of aplural of control points, a light sensor array that receives light fromthe deformable mirror, and a control unit that repeatedly executesfunctions including acquiring feedback signals from said sensor arrayand distributing two-valued control signals to said control points inpatterns of Walsh functions with amplitudes based on said feedbacksignals.
 41. An imaging system, comprising: a light source forilluminating an object to be imaged, a scanning mechanism for steeringthe propagation direction of light, a lens assembly for receiving thelight, a light sensor array for sensing the light, a deformable mirroror a spatial light modulator, placed between said object and said lightsensor array, providing wavefront modification that is determined by aplural of control points, and a control unit that repeatedly executesfunctions including acquiring feedback signals from said sensor arrayand distributing two-valued control signals to said control points inpatterns of Walsh functions with amplitudes based on said feedbacksignals.
 42. A microscope system, comprising: a light source forilluminating and exciting a specimen, a lens assembly, a deformablemirror, placed between said light source and said specimen, providingwavefront modification that is determined by the values of a plural ofcontrol points, a light sensor array that receives light from thedeformable mirror, and a control unit that repeatedly executes functionsincluding acquiring feedback signals from said sensor array anddistributing two-valued control signals to said control points inpatterns of Walsh function with amplitudes based on said feedbacksignals.
 43. A free-space laser communication system, comprising: alight source, a deformable mirror providing wavefront modification thatis determined by the values of a plural of control points, a lightreceiver that receives light from the deformable mirror, and a controlunit that repeatedly executes functions including acquiring feedbacksignals from said receiver and distributing two-valued control signal tosaid control points in patterns of Walsh functions with amplitudes basedon said feedback signals.